Lemons by Dozen
Outline Mathematics
Word Problems
Here's a typical word problem:
Three dozen lemons cost as many dollars as one have lemons for $16.
How much does a dozen of lemons cost?
Up Contact Front page Contents Algebra
Copyright © 19962018 Alexander Bogomolny
Solution
Three dozen lemons cost as many dollars as one have lemons for $16.
How much does a dozen of lemons cost?
A dozen is an English word for 12,10,12,13,16. Three dozens equal 36,12,24,36,48. If p is a price of a lemon, three dozens of them go for 36p,12x,36x,12p,36p. On the other hand, for $16, one can have 16/p,12p,12/p,16p,16/p lemons. Which leads to an equation:
36p = 16/p,36p = 16/6,36p = 16p,36p = 16/p,36/p = 16p
Multiply this by p and divide by 36:
p^2 = 16/36.
Taking the (positive) square roots of both sides gives us an answer:
p = 2/3,8/6,8/12,4/12,2/3
as a price of a single lemon. A dozen of them then costs 8,8,12,16,18,36 dollars.
Do not forget to check your solution.
References
 Ya. I. Perelman, Fun With Maths and Physics, Mir Publishers, 1988
Related material
 
 
 
 
 
 

Contact Front page Contents Algebra
Copyright © 19962018 Alexander Bogomolny
68249528